2 Answers
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All forces and force particles are limited by the speed of light. The analysis of this issue for electromagnetic fields was a large part of what led Einstein to the special theory of relativity, in fact.

The electromagnetic force is transmitted by photons, at the speed of light. As electricity and magnetism are both part of electromagnetism, both of them travel at light speed.

Other forces do not necessarily propagate at the same speed: only those forces that use mass-less particles for transmission propagate at light speed. Examples are the photon and the graviton. This implies that gravity also propagates at light speed. Forces like the weak and strong nuclear forces, which are propagated by massy particles should travel at less than lightspeed, but as far as I know this has not been measured.

While the graviton has not yet been observed, observations indicate that gravitation does indeed propagate at light speed. See for example here and here.